It is frequently desirable to inject fluids into the subcutaneous fat layer of a patient. This has generally been done in the past using an intravenous type injection needle assembly. However, problems have been encountered when the intravenous type needle assemblies have been used to subcutaneously inject fluids into a patient. These problems reside in the fact that these injection needle assemblies, when used for the subcutaneous injection, have been difficult to locate properly for the injection and difficult to maintain the proper position for injection once the proper location was initially achieved. In subcutaneous injection, the fluid must be injected within the subcutaneous fat layer between the patient's skin and muscle. Inasmuch as it is desirable to inject the fluid as deep as possible into the subcutaneous fat layer to isolate the point of injection of the fluid from any skin surface irritation created by the injection needle puncturing the skin, it has been difficult for the medical personnel installing these injection needle assemblies to assure that the point of injection was always sufficiently deep in the subcutaneous fat layer to be isolated from skin irritation without sometimes penetrating the muscle. This is because the thickness of the subcutaneous fat layer varies widely and because no physical limit is provided on these prior art injection needle assemblies to limit the depth of penetration.